Hermite-Birkhoff interpolation on scattered data on the sphere and other manifolds

The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-05
Main Authors: Allasia, Giampietro, Cavoretto, Roberto, De Rossi, Alessandra
Format: Article
Language:English
Subjects:
Basis functions
Construction methods
Interpolation
Linear systems
Manifolds
Thermal expansion
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the interpolated function at the interpolation points. The basis functions depend on the geodesic distance, are orthonormal with respect to the point-evaluation functionals, and have all derivatives equal zero up to a certain order at the interpolation points. A remarkable feature of such interpolants, which belong to the class of partition of unity methods, is that their construction does not require solving linear systems. Numerical tests are given to show the interpolation performance.
ISSN:2331-8422